Exposure: Current, Potential Future and Exposure at Default

Exposure at default is an estimate of how much will still be outstanding on the day the other side fails, and it is almost never the balance that can be read today. On counterparty C1 the invented bank builds it from Rs 1,680 crore drawn, Rs 360 crore of the undrawn line, and Rs 120 crore on the derivative position. Rs 2,160 crore.

The whole subject rests on one shift, and the shift is worth making before any arithmetic. A balance is a fact about today, and a bank does not lose money today. The loss lands on a day nobody has picked yet, and on that day the line will have been drawn further than it is now and the contract will be worth something different from what it is worth this morning. So the question a credit officer is actually asking is not what is outstanding. The credit officer needs what will be outstanding then. Every step in the build-up below exists because somebody insisted on asking the second question rather than the first.

The counterparty throughout is C1, Nirjhar Industries Limited, an invented steel and alloys maker and the largest single-name exposure at Vindhya Commercial Bank Limited, an invented bank. Every amount that follows is in Rs crore. C1 carries Rs 1,680 crore drawn, an undrawn committed line of Rs 720 crore, and derivative trades with the bank. The counterparty table reports a total exposure of Rs 2,496 crore against C1. The exposure at default is Rs 2,160 crore. Both figures are correct, both describe one name on one day, and the Rs 336 crore between them is the whole subject.

Why is an exposure a forecast rather than a balance?

Start with something a reader can feel before any bank appears. A shopkeeper has extended credit to a regular customer. Rs 40,000/- is outstanding on the account this evening, and that figure is a fact: it is written in the book, it can be counted, and two people agree on it. Now ask the shopkeeper a different question. If that customer stops paying altogether, what will be outstanding on the day it happens? The answer is not Rs 40,000/-. The answer is Rs 40,000/- plus whatever the customer takes on credit between now and then, and a customer heading for trouble buys more on credit rather than less. The evening balance is a reading, and the number the shopkeeper actually needs is a forecast made of that reading plus a judgement about behaviour.

A bank is that shopkeeper at Rs 96,000 crore. Exposure at defaultAn estimate of how much will be outstanding at the moment the other side fails, which is a forecast and not a balance. is the name for the forecast, and it has one job: to say how much of the bank's money is standing in front of the counterparty on the day the counterparty stops paying. Three things go into that on C1, and only one of the three is a balance.

The first is the funded exposureMoney already lent and outstanding, which is the only part of an exposure that is a fact rather than an estimate. of Rs 1,680 crore. The funded exposure is money out of the door. The amount sits on the balance sheet, it can be counted, and no assumption anywhere in the build changes it. The second is the undrawn committed lineMoney the bank has promised and the borrower has not yet taken, which a borrower in trouble tends to take. of Rs 720 crore. The bank has promised that money and C1 has not taken it. On a balance sheet that is nothing at all. On the day of default it is very likely to be something. The third is the derivative position. The position has a value today and will have a different value later, and neither the bank nor C1 knows which way.

The third pair of bars in that drawing, set against the first, carries the point. The funded row is enormous and nothing happens to it. The undrawn row halves. The derivative row rises, and it rises by so little at this scale that the movement has to be pointed out. Two of the three rows change between the reading and the forecast. The row that changes by the smallest amount causes the most confusion in practice, and it does so because it is the only row where the same position carries two different correct numbers with two different names. The three rows come apart in turn below.

What would be lost if the other side failed today?

Current Exposure: what the contract is worth right now, and why a losing trade is worth nothing

Current exposureWhat would be lost if the other side failed today, being the positive value of the contract and nothing else. answers exactly one question, and it is the easy half of the measure: if C1 stopped paying this morning, how much would Vindhya Commercial Bank Limited be out of pocket on its derivative trades? The answer can be read rather than estimated. Being readable is what makes it the easy half. The measure takes what the contracts are worth today and counts the part that is worth something to the bank.

C1 has two trades with the bank. One is worth plus Rs 132 crore to the bank and one is worth minus Rs 36 crore. Both figures are the invented bank's own. Now hold the second one still for a moment. Everything difficult about current exposure lives in it. The losing trade is out of the moneyA contract whose current value is against the holder, which is worth nothing to that holder if the other side fails. from the bank's side: if it were settled this morning the bank would pay Rs 36 crore rather than receive it.

Now ask what becomes of that losing trade if C1 fails. The bank does not collect on it. There is nothing to collect: the bank is the side that would have to pay. So the losing trade adds nothing at all to what the bank loses. A contract that is out of the money is worth nothing in the other side's default. Current exposure therefore floors at zero on each contract and never runs negative. The floor is not an accounting convention and it is not conservatism. The floor follows from what a default is. An amount that was never going to be received is not an amount that can be lost.

So the un-netted reading is Rs 132 crore. The two trades stand alone, the winner counts in full and the loser counts as nothing. A netting agreement changes the legal unit rather than the values: the two trades stop being two claims and become one, so they are added together before the floor is applied. Rs 132 crore less Rs 36 crore is Rs 96 crore, a fall of 27.3 per cent. The definition of a netting agreement and the test that makes one enforceable are settled under netting agreements, and both enter here as facts about C1.

One warning about the number Rs 132 crore before it is carried anywhere. The bank's records hold two of them. Rs 132 crore is C1's un-netted current exposure, the figure the drawing above sets out. Rs 132 crore is also the total derivative current exposure of the four counterparties in this book that carry one with no netting agreement recorded, being C3 at Rs 24 crore, C5 at Rs 12 crore, C7 at Rs 36 crore and C10 at Rs 60 crore. The two are the same number and have nothing else whatever in common, so which one is meant has to be named every single time it is written down.

What is the contract likely to be worth before it ends?

Potential Future Exposure: an allowance for a move that has not happened yet

Current exposure has a hole in it, and it is a large one. The measure answers what would be lost if C1 failed this morning, and C1 is not going to fail this morning. The trades run on for months. Over those months the value of the position moves, and the direction that matters to the bank is upward. A position that moves in the bank's favour is a position on which the bank stands to lose more if C1 then fails. Current exposure measures a loss the bank would take today, and the contract is going to sit there for a long time after today, so something has to stand in for the part of the life of the contract that has not happened.

The stand-in is potential future exposureAn allowance for how far the value of a contract could move in the bank's favour before it ends., and the invented bank computes it the simple way: as an add-onA percentage applied to the size of a contract, not to its value, to estimate potential future exposure.. Vindhya Commercial Bank Limited applies 1.5 per cent, its own factor rather than anybody's published one, to a notionalThe contract size a percentage is applied to, which is not an amount anybody owes. of Rs 1,600 crore on C1's trades. The product is Rs 24 crore.

Now the part worth slowing down for. Most readers first go wrong here. Look at what the percentage was applied to. Not the Rs 96 crore the position is worth. The Rs 1,600 crore the contract is sized at. The two figures are wildly different, and the second one is not an amount anybody owes anybody: a notional is the reference size the payments on a contract are computed from, and no part of it changes hands. The estimate is of how far the value could travel, so the add-on is taken on the size of the contract rather than on its current value. Travel depends on how big the contract is and not on where the value happens to be sitting today.

The extreme case is the fastest way to feel it. Suppose C1's position were worth exactly nothing this morning, right on the zero line. A percentage taken on value would give an add-on of zero, and the bank would be saying that a contract which has not moved yet can never move. The claim is plainly false, and it is false in the most dangerous direction: a Rs 1,600 crore contract sitting at zero has a great deal of room in both directions and the bank would have measured none of it. The limit on the travel is the size of the contract, not the reading on it, so a contract worth nothing today and a contract worth Rs 96 crore today can travel exactly the same distance over the next year.

The two halves together make the derivative measure the bank actually uses. Rs 96 crore of netted current exposure plus Rs 24 crore of potential future exposure is Rs 120 crore, and that Rs 120 crore is C1's derivative exposure at default. The Rs 120 crore is worth holding on to. The counterparty table does not carry it, and one of the most common errors on this subject is reading the table figure as though it were this one.

How do the two halves of the measure differ, and where do they meet?

Current Exposure Vs Potential Future Exposure: one has already happened and one has not

Set the two side by side. The difference between them is not a matter of degree. Current exposure is a reading. Somebody values the trades, applies the floor, applies the netting agreement, and writes down Rs 96 crore. Two people doing that carefully will agree. Potential future exposure is an estimate. Somebody decides how far a Rs 1,600 crore contract could travel in the time it has left, expresses that decision as 1.5 per cent, and writes down Rs 24 crore. Two careful people can disagree about the second number and both be defensible. The number describes a move that has not occurred and may never occur.

The whole distinction is worth naming plainly. Current exposure is the value a contract carries today and can be read off the trades, and potential future exposure is the value it could carry before it matures and has to be estimated. The exposure that must be estimated rather than read is the entire difference between plain credit risk and counterparty risk. A term loan has a balance, and the balance is the exposure. A derivative has a value that moves on both sides of zero for years, and no balance describes it.

Here is the part a table can never show. The two halves are measured on completely different scales. Current exposure is measured on value, so a netting agreement that removes Rs 36 crore of value removes Rs 36 crore of exposure. Potential future exposure is measured on contract size, so it does not care about value at all and does not move when netting does. A benefit won on one scale can therefore be handed straight back on the other, and the point where that happens is computable. At an add-on factor of 2.25 per cent the add-on is Rs 36 crore, exactly what the netting agreement removed, so the derivative exposure at default returns to the un-netted Rs 132 crore and the netting benefit is cancelled outright. The bank's own factor is 1.5 per cent, so it is not sitting far from that point.

There is a second computable point further along and it asks a harder question. At an add-on factor of 6.0 per cent the add-on is Rs 96 crore, exactly equal to the netted current exposure. At that setting half the derivative measure is a loss that would land today and half is an allowance for a move nobody has seen. The mix is the question to stop on: how much of the measure is fact and how much is allowance. At the invented bank's own 1.5 per cent the split is Rs 24 crore against Rs 96 crore, one part forecast to four parts fact. Neither setting is right or wrong here. The mix is a choice somebody made, and the choice is invisible in the total.

One crossing that people expect is not there, and its absence is worth stating. The bank's own single name limit L1 stands at Rs 2,640 crore. C1's total exposure at default is Rs 2,136 crore plus sixteen times the factor, so reaching L1 on this basis would need an add-on factor of 31.5 per cent. No bank sets a factor anywhere near that. On the exposure at default basis this counterparty stays under its own single name limit at every add-on factor a bank would actually use, so there is no crossing to look for.

What does a line the borrower has not drawn contribute to the exposure?

Leave the derivative alone for a while. Everybody finds it interesting, and it is not the part that carries the money. C1 has an undrawn committed line of Rs 720 crore. The bank has promised it. C1 has not taken it. On the balance sheet it is nothing: no asset, no interest, no cash gone.

Here is the everyday version, and it stays in the mind longer than the arithmetic. A cousin has promised that if Rs 2,00,000/- is ever needed it is there for the asking, and not a rupee of it has been asked for. Right now the cousin is out Rs 0/-. The day the promise is actually called is not a day when things are going well. The call comes on the day the job ended or the hospital bill arrived. The promise is worth nothing on every ordinary day and worth its full size on precisely the day it is called, and the day it is called is the bad day. An undrawn line is therefore never zero in a credit officer's mind, even though it is zero on the balance sheet.

A borrower heading for default behaves the same way and for the same reason. Cash gets tight, the ordinary sources close one by one, and the line that has already been agreed and needs no fresh approval is the cheapest and fastest money left in the building. So the bank makes an assumption about how much of it will be gone by the time the default arrives. Vindhya Commercial Bank Limited applies a drawdown assumptionThe share of an undrawn line a lender assumes will be drawn before default, here the bank's own 50.0 per cent. of 50.0 per cent, its own figure rather than a published one. Half of Rs 720 crore is Rs 360 crore, and that Rs 360 crore joins the exposure at default.

The comparison worth making sets that Rs 360 crore next to the derivative position. The half of the undrawn line the bank expects to be taken is Rs 360 crore, three times the Rs 120 crore of derivative exposure at default, so on this counterparty the promise the bank made is a bigger part of what is at risk than every trade it has ever done with the name. The derivative gets the attention because it is the part with the interesting arithmetic. The promise gets forgotten because there is nothing to compute until somebody makes an assumption.

Everything about that Rs 360 crore turns on the 50.0 per cent, and the 50.0 per cent is a choice. Running the two ends of it shows how much of the answer that single decision carries. At a drawdown assumption of zero, meaning the bank believes a defaulting borrower takes nothing more, C1's exposure at default is Rs 1,800 crore. At 100 per cent, meaning the borrower empties the line before it fails, it is Rs 2,520 crore. The range is Rs 720 crore wide and one assumption drives all of it, against which the entire derivative position, netting agreement, notional, add-on and all, moves the answer by Rs 120 crore. The part of the measurement everybody argues about is the smaller part by a factor of six.

How does the whole build come together on one counterparty?

Now put the four steps in order. Seeing them as a sequence is what stops the total from looking like a single measurement. Counterparty C1 is Nirjhar Industries Limited, a steel and alloys maker, internal grade 4, and the largest single-name exposure in this invented bank's book. Everything below is in Rs crore and every figure belongs to the invented bank.

Read the third column before the fourth. Only one of the four steps is a fact, one is a reading taken this morning, and two are assumptions somebody at the bank chose and could have chosen differently. The total says Rs 2,160 crore with the confidence of a measured quantity, and Rs 384 crore of it, being the Rs 360 crore of undrawn line and the Rs 24 crore of add-on, exists only because two decisions were made. The choosing is not a criticism of the number. The number is made of those choices. A reader who takes the Rs 2,160 crore and never asks which parts were chosen has taken somebody's judgement and treated it as a measurement.

How does this differ from the other two numbers in the expected loss computation?

Probability of Default vs Loss Given Default vs Exposure at Default: three properties of three different things

Exposure at default almost never travels alone. Exposure at default is one of three numbers a bank multiplies together to size an expected loss, and the three get confused constantly, usually because they arrive in the same sentence and are all expressed as numbers. The three are not the same kind of thing at all. Each answers a different question and each is a property of a different object.

Probability of default answers how likely. The question is whether this borrower fails in the next year, and the answer is a property of the borrower: its business, its cash generation, its balance sheet, expressed through the grade the bank has assigned. C1 is grade 4 and the bank's own one-year figure for grade 4 is 0.45 per cent. Loss given default answers how much of it is lost. The question is what share of the outstanding amount never comes back after the failure, and the answer is a property of the recovery: the security it holds, the enforcement it can run, the queue it stands in. The bank assumes 40.0 per cent before collateral, its own figure again. Exposure at default answers how much is outstanding when it happens, and it is a property of the facility and the contract rather than of the borrower at all. Probability of default belongs to the borrower, loss given default belongs to the recovery, and exposure at default belongs to the facility, so the only operation that makes sense across the three is multiplication.

Multiplying them on C1 gives the expected loss. Rs 2,160 crore times 0.45 per cent times 40.0 per cent is Rs 3.89 crore, uncollateralised. The Rs 3.89 crore is small next to a Rs 2,160 crore exposure and it is meant to be: expected loss is the amount a bank prices for and provides against in the ordinary course, not the amount it would actually lose if C1 failed. If C1 fails, the bank does not lose Rs 3.89 crore. The bank loses something in the region of 40.0 per cent of Rs 2,160 crore. The Rs 3.89 crore is what that outcome is worth today given that it probably does not happen.

The reason this matters is that a report will try to rank counterparties on one of the three, and a ranking on one factor of a three-way product is not a ranking of risk. The bank's own rating scale contains the cleanest possible demonstration: grade 7 carries a 3.60 per cent probability on Rs 4,704 crore of exposure and grade 8 carries a 7.20 per cent probability on Rs 2,352 crore, and both produce exactly Rs 67.74 crore of expected loss. The probability doubles, the exposure halves, and the money is identical to the paisa. Anyone ordering those two grades by probability alone has produced an order the money does not support.

Where does the reading of this go wrong in practice?

Can the same build be run across the whole book?

The honest answer is not fully. Part of the build runs across the whole book and part of it stops. The funded and undrawn parts come first. Both of those work. Across the ten largest single names the funded exposure is Rs 9,960 crore and the undrawn lines are Rs 2,880 crore. Applying the bank's own 50.0 per cent gives Rs 1,440 crore of assumed drawdown across the ten names, so the credit-equivalent exposure on the loan side of the book is Rs 11,400 crore. The Rs 11,400 crore is computable from the record and reproducible by anybody holding it.

The derivative side stops. Five of the ten carry derivative current exposure: C1 at Rs 96 crore, C3 at Rs 24 crore, C5 at Rs 12 crore, C7 at Rs 36 crore and C10 at Rs 60 crore, totalling Rs 228 crore. Turning any of those into an exposure at default requires a notional and an add-on factor for each position, and this record carries them for C1 alone. The exposure at default of C3, C5, C7 and C10 is not unknown because nobody has bothered: it is not computable from what exists, and the correct thing to write down is that the measurement was not made. Rs 11,400 crore plus C1's Rs 120 crore plus the other four counterparties at their current exposure of Rs 132 crore comes to Rs 11,652 crore, and that figure has to be labelled a floor rather than a total.

Notice the second Rs 132 crore has just walked back in, and this time it is the sum across C3, C5, C7 and C10 rather than C1's un-netted reading. The two are different objects that happen to share a number. Notice also which name is the most derivative-heavy: C10 at Rs 60 crore of derivative current exposure against a total exposure of Rs 780 crore is 7.7 per cent, higher than C1's 3.8 per cent, and C10 is the smallest name on the list. The exposure that is hardest to measure is not the exposure that is largest.

Who actually uses this number, and what do they do with it?

Three people pick up an exposure at default and do three different things with it. Watching the three is the fastest way to see the purpose of the measure.

The credit officer inside the bank uses it to answer whether more can be lent. C1 sits against limit L1, the bank's own single name limit of Rs 2,640 crore. Measured against the reported total of Rs 2,496 crore that limit runs at 94.5 per cent, close enough to be a live conversation. Measured against the exposure at default of Rs 2,160 crore the same limit runs at a comfortable 81.8 per cent. One counterparty, one day, one limit, and 12.7 percentage points depending only on which measure the limit is written against, so the wording of the limit decides the answer before anybody computes anything. The gap of Rs 336 crore is the undrawn line taken at half rather than in full, being Rs 360 crore, less the derivative measure rising from Rs 96 crore to Rs 120 crore, being Rs 24 crore.

The analyst outside the bank uses it to judge whether the disclosure can be trusted. The drawdown assumption, the notional and the add-on factor are internal, so she cannot recompute this bank's exposure at default. She can still ask which basis the published table is drawn on, ask whether the same basis is used for the limit, and notice that a bank publishing derivative current exposure without a notional anywhere has published a number nobody outside can extend. The three questions cost nothing, and they separate a report that has thought about the measurement from one that has copied last quarter's format.

And now the household version. The mechanism is identical at every scale. Somebody working out what they owe adds the loan balance and the card balance and stops. Left out are the limit on the card they have not used, the overdraft the bank agreed and they have forgotten, and the personal loan a relative has promised. On an ordinary month all three are zero. On the month everything goes wrong all three are drawn, and the true figure was never the sum of the balances. The true figure was the sum of the balances plus a judgement about which promises get called. Exposure at default is that judgement, written down, applied consistently, and given a number so that somebody else can argue with it.